scholarly journals An Efficient Structural Technique for Encoding 'Best-fit' Straight Lines

1987 ◽  
Vol 30 (2) ◽  
pp. 168-175 ◽  
Author(s):  
C. M. A. Castle
Keyword(s):  
Straight Lines ◽  
Best Fit

An Analysis of the Shape and Propagation of Waves on the Flagellum of Crithidia Oncopelti

1979 ◽  
Vol 80 (1) ◽  
pp. 299-315
Author(s):  
D. N. JOHNSTON ◽  
N. R. SILVESTER ◽  
M. E. J. HOLWILL
Keyword(s):  
Back Projection ◽  
Active Process ◽  
Automatic Data ◽  
Circular Arcs ◽  
Fourier Series Method ◽  
Dark Ground ◽  
Propagation Of Waves ◽  
Straight Lines ◽  
Best Fit ◽  
Automatic Data Acquisition

Ciné micrographs were taken of the flagellated protozoan Crithidia oncopelti under dark-ground illumination. Coordinates of images of the flagella were obtained from the ciné frames by back-projection and automatic data acquisition. The flagellar waveforms of proximally directed waves were characterized using a Fourier-series method and compared by this means with a number of analytical curves. The shape of a wave remained constant as it was propagated and, of the curves suggested, a wave consisting of circular arcs connected by straight lines gave the best fit. The variation of bend curvature as bends moved along the flagellum was also found, for both proximally and distally directed waves. The wavelengths and speeds of proximally directed waves increased linearly with distance as they approached the base of the flagellum, while in distally directed bends the curvature remained constant but the velocity increased as bends moved away from the base. Causes of the above behaviour are discussed and it is concluded from the variation of curvature with time for proximally directed flagellar waves that unbending must be an active process.

scholarly journals Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

2008 ◽  
Vol 8 (2) ◽  
pp. 6409-6436 ◽  
Author(s):  
C. A. Cantrell
Keyword(s):  
Least Squares ◽  
Atmospheric Chemistry ◽  
Least Squares Method ◽  
Technical Note ◽  
Routine Practice ◽  
Data Sets ◽  
Straight Line ◽  
Sample Data ◽  
Straight Lines ◽  
Best Fit

Abstract. The representation of data, whether geophysical observations, numerical model output or laboratory results, by a best fit straight line is a routine practice in the geosciences and other fields. While the literature is full of detailed analyses of procedures for fitting straight lines to values with uncertainties, a surprising number of scientists blindly use the standard least squares method, such as found on calculators and in spreadsheet programs, that assumes no uncertainties in the x values. Here, the available procedures for estimating the best fit straight line to data, including those applicable to situations for uncertainties present in both the x and y variables, are reviewed. Representative methods that are presented in the literature for bivariate weighted fits are compared using several sample data sets, and guidance is presented as to when the somewhat more involved iterative methods are required, or when the standard least-squares procedure would be expected to be satisfactory. A spreadsheet-based template is made available that employs one method for bivariate fitting.

scholarly journals Technical Note: Review of methods for linear least-squares fitting of data and application to atmospheric chemistry problems

2008 ◽  
Vol 8 (17) ◽  
pp. 5477-5487 ◽  
Author(s):  
C. A. Cantrell
Keyword(s):  
Least Squares ◽  
Atmospheric Chemistry ◽  
Least Squares Method ◽  
Technical Note ◽  
Routine Practice ◽  
Data Sets ◽  
Straight Line ◽  
Sample Data ◽  
Straight Lines ◽  
Best Fit

Abstract. The representation of data, whether geophysical observations, numerical model output or laboratory results, by a best fit straight line is a routine practice in the geosciences and other fields. While the literature is full of detailed analyses of procedures for fitting straight lines to values with uncertainties, a surprising number of scientists blindly use the standard least-squares method, such as found on calculators and in spreadsheet programs, that assumes no uncertainties in the x values. Here, the available procedures for estimating the best fit straight line to data, including those applicable to situations for uncertainties present in both the x and y variables, are reviewed. Representative methods that are presented in the literature for bivariate weighted fits are compared using several sample data sets, and guidance is presented as to when the somewhat more involved iterative methods are required, or when the standard least-squares procedure would be expected to be satisfactory. A spreadsheet-based template is made available that employs one method for bivariate fitting.

scholarly journals Is the Best Fitting Curve Always Unique?

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
N. Chernov ◽  
Q. Huang ◽  
H. Ma
Keyword(s):  
Computer Vision ◽  
Errors In Variables ◽  
Basic Task ◽  
Data Points ◽  
Best Fitting ◽  
Straight Lines ◽  
Best Fit ◽  
Curved Objects

Fitting straight lines and simple curved objects (circles, ellipses, etc.) to observed data points is a basic task in computer vision and modern statistics (errors-in-variables regression). We have investigated the problem of existence of the best fit in our previous paper (see Chernov et al. (2012)). Here we deal with the issue of uniqueness of the best fit.

Physiologic determinants of left ventricular strength-interval curve of the dog

1977 ◽  
Vol 233 (5) ◽  
pp. H555-H561 ◽  
Author(s):  
A. V. Goodyer ◽  
B. Y. Wong
Keyword(s):  
Venous Return ◽  
Left Ventricular Pressure ◽  
Left Ventricular ◽  
Ventricular Pressure ◽  
High Fidelity ◽  
Ventricular Pacing ◽  
Arterial Blood ◽  
Premature Beats ◽  
Straight Lines ◽  
Best Fit

Strength-interval curves, relating an index of the contractile vigor of premature beats to their coupling intervals, were elicited in anesthetized, open-chest dogs prepared for atrial or ventricular pacing and the high-fidelity measurement of left ventricular pressure. During inotropic interventions, changes of the curves were evaluated in terms of the parameters (slopes and intercepts) of their straight lines of best fit. These parameters were altered by isoproterenol, propranolol, and heart rate, and were correlated closely with paired values of isovolumic Vmax (of driven beats). The strength-interval curves were reproducible and were not affected by large changes of venous return or arterial blood pressure. These results provide a basis for the use of strength-interval curves for the evaluation of ventricular contractile state, using fluid-filled catheters for the measurement of left ventricular pressure.

Correlation of N.M.R. shifts with chemical reactivity in phenethyl systems

1974 ◽  
Vol 27 (10) ◽  
pp. 2283 ◽  
Author(s):  
LF Blackwell ◽  
PD Buckley ◽  
KW Jolley
Keyword(s):  
Rate Constants ◽  
Chemical Shifts ◽  
Chemical Reactivity ◽  
Leaving Group ◽  
Straight Lines ◽  
Best Fit

Correlations between 1H substituent-induced chemical shifts (scs) for α- and β-methylene protons in, and rate constants for base-catalysed E2 elimination from, substituted phenethyl bromides and dimethyl(phenethyl)sulphonium bromides have been obtained. The slopes of the best-fit straight lines were similar in all cases for the β-methylene protons but were found to vary with the leaving group for the α-methylene protons.

Domain Formation in Synthetic Quartz

1971 ◽  
Vol 29 ◽  
pp. 156-157
Author(s):  
Joseph J. Comer
Keyword(s):  
Electron Beam ◽  
Room Temperature ◽  
Domain Formation ◽  
Synthetic Quartz ◽  
Transmission Electron ◽  
Black Spots ◽  
Diffraction Mode ◽  
Domain Boundaries ◽  
Kikuchi Lines ◽  
Straight Lines

Domains visible by transmission electron microscopy, believed to be Dauphiné inversion twins, were found in some specimens of synthetic quartz heated to 680°C and cooled to room temperature. With the electron beam close to parallel to the [0001] direction the domain boundaries appeared as straight lines normal to <100> and <410> or <510> directions. In the selected area diffraction mode, a shift of the Kikuchi lines was observed when the electron beam was made to traverse the specimen across a boundary. This shift indicates a change in orientation which accounts for the visibility of the domain by diffraction contrast when the specimen is tilted. Upon exposure to a 100 KV electron beam with a flux of 5x 1018 electrons/cm2sec the boundaries are rapidly decorated by radiation damage centers appearing as black spots. Similar crystallographio boundaries were sometimes found in unannealed (0001) quartz damaged by electrons.

Question Wording Effects in the Assessment of Global Self-Esteem

2000 ◽  
Vol 16 (1) ◽  
pp. 13-19 ◽  
Author(s):  
Martin Dunbar ◽  
Graeme Ford ◽  
Kate Hunt ◽  
Geoff Der
Keyword(s):  
Reading Ability ◽  
Factor Model ◽  
Self Esteem ◽  
Reading Scores ◽  
Poor Reading ◽  
Method Effect ◽  
Two Samples ◽  
Positive Item ◽  
Method Effects ◽  
Best Fit

Summary: Marsh (1996) produced evidence that method effects associated with negatively worded items might be responsible for the results of earlier factor analytic studies that reported finding positive and negative self-esteem factors in the Rosenberg Global self-esteem scale ( Rosenberg, 1965 ). He analyzed data collected from children using a 7-item self-esteem measure. This report details attempts to replicate Marsh 's analysis in data collected from two samples of adults who completed the full 10-item Global Self-Esteem (GSE) scale. The results reported here are similar to those given by Marsh in so much as a correlated uniquenesses model produced a superior fit to the data than the simple one factor model (without correlated uniquenesses) or the often reported two factor (positive and negative self-esteem) model. However, whilst Marsh reported that the best fit was produced by allowing negative item uniquenesses to correlate with each other, the model that produced the best fit to these data was one that contained correlated positive item uniquenesses. Supporting his claim that differential responding to negative and positive self-esteem items reflects a method effect associated with reading ability, Marsh also showed that factors associated with negative and positive items were most distinct among children who had poor reading scores. We report a similar effect among a sample of older adults where the correlation between these factors was compared across two groups who were selected according to their scores on a test of verbal reasoning.

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